I asked a similar question on another forum, and someone suggested that older bikes, that pre-date the spark arrestor requirement, do not need them. Unfortunately, I can't find any indication of such an exemption on any Forest Service, BLM or State Trails sites. They all indicate that all motorcycles must have spark arrestors if they are used on lands belonging to those agencies.
I agree that four-stroke bikes are far less likely to start a fire, since there is so little unburnt fuel exiting their tailpipes, but the spark arrestor requirement is really meant to catch bits of hot carbon, like the stuff that builds up on your plugs and valves when your fuel mixture is over-rich. Those bits of carbon build up in four-strokes too, just not as predictably as with two-strokes.
I'd like to make my 1970 CB350 legal to operate in the forest, but I can't find any sort of universal spark arrestor that looks remotely like stock CB350 pipes. I don't want to bolt a couple of mufflers on the bike that are designed for some modern dirt bike. I've thought about switching to CL350 pipes, but I can't confirm that they are approved spark arrestors either.